Interlacements and the wired uniform spanning forest
From MaRDI portal
Publication:1746152
DOI10.1214/17-AOP1203zbMATH Open1391.60021arXiv1512.08509OpenAlexW3103172259MaRDI QIDQ1746152
Author name not available (Why is that?)
Publication date: 24 April 2018
Published in: (Search for Journal in Brave)
Abstract: We extend the Aldous-Broder algorithm to generate the wired uniform spanning forests (WUSFs) of infinite, transient graphs. We do this by replacing the simple random walk in the classical algorithm with Sznitman's random interlacement process. We then apply this algorithm to study the WUSF, showing that every component of the WUSF is one-ended almost surely in any graph satisfying a certain weak anchored isoperimetric condition, that the number of `excessive ends' in the WUSF is non-random in any graph, and also that every component of the WUSF is one-ended almost surely in any transient unimodular random rooted graph. The first two of these results answer positively two questions of Lyons, Morris and Schramm, while the third extends a recent result of the author. Finally, we construct a counterexample showing that almost sure one-endedness of WUSF components is not preserved by rough isometries of the underlying graph, answering negatively a further question of Lyons, Morris and Schramm.
Full work available at URL: https://arxiv.org/abs/1512.08509
No records found.
No records found.
This page was built for publication: Interlacements and the wired uniform spanning forest
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1746152)
